Estimate conditional probability densities using smoothing spline
ANOVA models. The symbolic model specification via formula
follows the same rules as in lm.
sscden(formula, response, type=NULL, data=list(), weights, subset,
na.action=na.omit, alpha=1.4, id.basis=NULL, nbasis=NULL,
seed=NULL, ydomain=as.list(NULL), yquad=NULL, prec=1e-7,
maxiter=30, skip.iter=FALSE)sscden1(formula, response, type=NULL, data=list(), weights, subset,
na.action=na.omit, alpha=1.4, id.basis=NULL, nbasis=NULL,
seed=NULL, rho=list("xy"), ydomain=as.list(NULL), yquad=NULL,
prec=1e-7, maxiter=30, skip.iter=FALSE)
sscden returns a list object of class "sscden".
sscden1 returns a list object of class
c("sscden1","sscden").
dsscden and cdsscden can be used to
evaluate the estimated conditional density \(f(y|x)\) and
\(f(y1|x,y2)\); psscden, qsscden,
cpsscden, and cqsscden can be used to
evaluate conditional cdf and quantiles. The methods
project.sscden or project.sscden1 can
be used to calculate the Kullback-Leibler or square-error
projections for model selection.
Symbolic description of the model to be fit.
Formula listing response variables.
List specifying the type of spline for each variable.
See mkterm for details.
Optional data frame containing the variables in the model.
Optional vector of counts for duplicated data.
Optional vector specifying a subset of observations to be used in the fitting process.
Function which indicates what should happen when the data contain NAs.
Parameter defining cross-validation scores for smoothing parameter selection.
Index of observations to be used as "knots."
Number of "knots" to be used. Ignored when
id.basis is specified.
Seed to be used for the random generation of "knots."
Ignored when id.basis is specified.
Data frame specifying marginal support of conditional density.
Quadrature for calculating integral on Y domain. Mandatory if response variables other than factors or numerical vectors are involved.
Precision requirement for internal iterations.
Maximum number of iterations allowed for internal iterations.
Flag indicating whether to use initial values of
theta and skip theta iteration. See ssanova for
notes on skipping theta iteration.
rho function needed for sscden1.
The model is specified via formula and response, where
response lists the response variables. For example,
sscden(~y*x,~y) prescribe a model of the form
$$
log f(y|x) = g_{y}(y) + g_{xy}(x,y) + C(x)
$$
with the terms denoted by "y", "y:x"; the term(s) not
involving response(s) are removed and the constant C(x) is
determined by the fact that a conditional density integrates to one
on the y axis. sscden1 does keep terms not involving
response(s) during estimation, although those terms cancel out when
one evaluates the estimated conditional density.
The model terms are sums of unpenalized and penalized terms. Attached to every penalized term there is a smoothing parameter, and the model complexity is largely determined by the number of smoothing parameters.
A subset of the observations are selected as "knots." Unless
specified via id.basis or nbasis, the number of
"knots" \(q\) is determined by \(max(30,10n^{2/9})\), which is
appropriate for the default cubic splines for numerical vectors.
Gu, C. (1995), Smoothing spline density estimation: Conditional distribution. Statistica Sinica, 5, 709--726. Springer-Verlag.
Gu, C. (2014), Smoothing Spline ANOVA Models: R Package gss. Journal of Statistical Software, 58(5), 1-25. URL http://www.jstatsoft.org/v58/i05/.
data(penny); set.seed(5732)
fit <- sscden1(~year*mil,~mil,data=penny,
ydomain=data.frame(mil=c(49,61)))
yy <- 1944+(0:92)/2
quan <- qsscden(fit,c(.05,.25,.5,.75,.95),
data.frame(year=yy))
plot(penny$year+.1*rnorm(90),penny$mil,ylim=c(49,61))
for (i in 1:5) lines(yy,quan[i,])
## Clean up
if (FALSE) rm(penny,yy,quan)
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